Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation
The dramatic effect of quantized vortices in superfluid helium on the rate of coalescence of suspended impurities has been predicted; such catalytic process should result in formation of fiber-like structures having primarily nanothickness. That should be valid for any impurity and it may be used as...
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nasplib_isofts_kiev_ua-123456789-1169932025-06-03T16:26:44Z Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation Gordon, E.B. Okuda, Y. Квантовые жидкости и квантовые кpисталлы The dramatic effect of quantized vortices in superfluid helium on the rate of coalescence of suspended impurities has been predicted; such catalytic process should result in formation of fiber-like structures having primarily nanothickness. That should be valid for any impurity and it may be used as a base for the universal method of nanowires and nanotubes producing. The experiments on molecular hydrogen imbedding into liquid helium supported these conclusions. They showed that: (i) in normal liquid He the coalescence led to formatting spherical microparticles carried by turbulent motion of a liquid; (ii) in the superfluid only very long filaments were observed, they behaved as quantized vortices should do. These filaments are fiber-like hydrogen crystals and they survived liquid helium transition to normal state. The promises for using this phenomenon in basic and applied sciences have been outlined. This work was supported in part by Russian Foundation for Basic Researches grant #07-03-00393. The authors are grateful to A.V. Karabulin for technical assistance and to Profs. I. Silvera (Harvard University), A. Weis (Fribourg University), and Y. Kagan (Kurchatov Centre) for valuable discussions. 2009 Article Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation / E.B. Gordon, Y. Okuda // Физика низких температур. — 2009. — Т. 35, № 3. — С. 278-283. — Бібліогр.: 14 назв. — англ. PACS: 67.25.dk, 61.46.Km, 67.63.Cd https://nasplib.isofts.kiev.ua/handle/123456789/116993 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы |
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Квантовые жидкости и квантовые кpисталлы Квантовые жидкости и квантовые кpисталлы Gordon, E.B. Okuda, Y. Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation Физика низких температур |
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The dramatic effect of quantized vortices in superfluid helium on the rate of coalescence of suspended impurities has been predicted; such catalytic process should result in formation of fiber-like structures having primarily nanothickness. That should be valid for any impurity and it may be used as a base for the universal method of nanowires and nanotubes producing. The experiments on molecular hydrogen imbedding into liquid helium supported these conclusions. They showed that: (i) in normal liquid He the coalescence led to formatting spherical microparticles carried by turbulent motion of a liquid; (ii) in the superfluid only very long filaments were observed, they behaved as quantized vortices should do. These filaments are fiber-like hydrogen crystals and they survived liquid helium transition to normal state. The promises for using this phenomenon in basic and applied sciences have been outlined. |
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Article |
| author |
Gordon, E.B. Okuda, Y. |
| author_facet |
Gordon, E.B. Okuda, Y. |
| author_sort |
Gordon, E.B. |
| title |
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation |
| title_short |
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation |
| title_full |
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation |
| title_fullStr |
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation |
| title_full_unstemmed |
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation |
| title_sort |
catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2009 |
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Квантовые жидкости и квантовые кpисталлы |
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https://nasplib.isofts.kiev.ua/handle/123456789/116993 |
| citation_txt |
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation / E.B. Gordon, Y. Okuda // Физика низких температур. — 2009. — Т. 35, № 3. — С. 278-283. — Бібліогр.: 14 назв. — англ. |
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Физика низких температур |
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2025-12-01T19:41:39Z |
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1850336192448430080 |
| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 3, p. 278–283
Catalysis of impurities coalescence by quantized vortices
in superfluid helium with nanofilaments formation
E.B. Gordon
Institute of Problems of Chemical Physics RAS, Chernogolovka 142432, Russia
E-mail: gordon.eb@gmail.com
Y. Okuda
Tokyo Institute of Technology, Tokyo 152-8551, Japan
Received October 31, 2008
The dramatic effect of quantized vortices in superfluid helium on the rate of coalescence of suspended
impurities has been predicted; such catalytic process should result in formation of fiber-like structures
having primarily nanothickness. That should be valid for any impurity and it may be used as a base for the
universal method of nanowires and nanotubes producing. The experiments on molecular hydrogen imbed-
ding into liquid helium supported these conclusions. They showed that: (i) in normal liquid He the
coalescence led to formatting spherical microparticles carried by turbulent motion of a liquid; (ii) in the
superfluid only very long filaments were observed, they behaved as quantized vortices should do. These
filaments are fiber-like hydrogen crystals and they survived liquid helium transition to normal state. The
promises for using this phenomenon in basic and applied sciences have been outlined.
PACS: 67.25.dk Vortices and turbulence;
61.46.Km Structure of nanowires and nanorods (long, free or loosely attached, quantum wires and
quantum rods, but not gate-isolated embedded quantum wires);
67.63.Cd Molecular hydrogen and isotopes.
Keywords: liquid helium, quantized vortices, molecular hydrogen, nanowire, flow tracer.
1. Introduction
Liquid and solid helium are the quantum liquid and
crystal correspondingly, thus all their characteristics are
spatially delocalized. The important and surprising
exclusion is the quantized vortices appeared in superfluid
helium in response to its excitation. Though a vortex
occupies whole liquid bulk its potential described by
formula
U
r
r
� ln
0
is noticeably distinguished from zero only in a vortex
core, its characteristic size r0 0 7� . � is even less than the
size of an atom. The quantized vortex length may be
meantime rather long and comparable with a vessel size
[1]. Any impurity including light helium isotope
3
He,
from one side, and rather large clusters, from another
side, tends to be placed in a vortex core because the
energy for a particle possessed the finite viscosity is
minimal at the axis of a vortex [2]. However the affinity
of these impurities to the vortex is rather small amounting
for atoms and small molecules to 3–10 K [1,3]. It means
that for the temperatures 1.5–2 K the probability to find
them inside of vortices is only weekly larger than outside,
though at T � 0.1 K practically all of them should be
finally attached to vortices. There are still no calculated
energies for binding larger features to a vortex in
literature but the authors of Ref. 4 found experimentally
that the preliminarily grown micron-size grains of
molecular hydrogen were concentrated steadily in
quantized vortices even in the very vicinity of � point,
i.e., at temperature around 2 K [4]. The problem the
authors of this paper put for themselves consisted in
revealing the possible role of quantized vortices not in
alignment of already prepared clusters, as it was already
done in Ref. 4 for visualization of quantized vortices in
© E.B. Gordon and Y. Okuda, 2009
superfluid helium, but in the very process of impurity
condensation into agglomerates and clusters.
A linear molecule of course tends to align along the
vortex axis [3]; this evidently should be true for a dimer
of atoms or molecules as well and the binding energy of a
dimer with a vortex has to be approximately twice as more
than for monomer. In general one could suppose that the
energy of small cluster pinning to a vortex is defined by
cluster length – for n links it will be n times more than for
individual particle. If so for the clusters or chains having
5–10 links the preference of their finding inside vortices
will be strongly dominant already at T � 2 K. Every guest
particles in liquid helium excluding
3
He stick together
practically at every collision, and the rate of condensation
governs by the rate of mutual collisions. The last is
proportional to square of impurity local density and thus
it much higher inside of vortex. The motion of captured
particles along the vortex core has no restriction; this
additionally enhances the rate of collisions because inside
of a vortex the particles can move only towards each
other, contrary to the bulk liquid helium where the
particle velocities are chaotically directed.
Such a way the presence of quantized vortices results
in sudden effect of catalysis of sedimentation for the
impurities — atoms, molecules and clusters — suspended
in superfluid helium. Provided the number of vortices is
sufficient the rate of the process as a whole should grow at
many orders of magnitude, and filament-like structures
should appear as a product of condensation.
2. Experimental evidences
These considerations were confirmed by our experi-
ments on imbedding the molecular hydrogen significantly
diluted by helium gas directly into superfluid helium; the
powerful gas jet provided a short time of mixture transport
to gas–liquid interface. This study has been performed in
Tokyo Institute for Physics and Technology [5]. The
4
He
cryostat has been equipped by two pairs of optical win-
dows and the inner diameter of its central bath was 160 mm
and the distance between the inner optical windows was
220 mm, the superfluid was achieved by pumping liquid
helium in the bath. The use of so large cryostat allowed to
be sure that both the vessel walls and liquid helium surface
were enough far away. To provide the reliable and fast
transport of impurity to liquid helium surface in the pre-
sence of large counterflow of evaporating helium we
applied gas helium jet technique [6]. Since the nearly
equimolecular mixture of hydrogen and deuterium formed
the particles which levitate in liquid helium the pre-
liminarily prepared gas mixture H2:D2:He = 1:1:200 was
used in the most of our experiments, though some sets were
performed for H2:He = 1:100 and D2:He = 1:100 mixtures.
A mixture at pressure of 3–6 bar was allowed with using of
electromagnetic valve to put into inlet capillary at pulses of
80 ms duration with repetition rate 6 Hz, 30–40 bursts in
each injection series. The total number of hydrogen
introduced into a fridge in sequence of pulses has been
chosen not so high to restrict the overlapping the structures
in the field of view. The molecular source was Dewar tube
with central capillary of 1 mm inner diameter and a nozzle
of about 300 �m at its bottom. The distance between the
nozzle and the surface of superfluid helium was 3–7 cm.
The sequence of pulsed jet entering liquid helium
significantly distorted its interface; the height of surface
waves was several mm and one could be positive that a lot
of quantized vortices appeared in He II just in the place
where density of guest particles was maximal. The optical
technique has been chosen for registration from the con-
sideration of reliability of interpretation. We understood
of course that because the spatial resolution of an optical
method can not be better than 1 �m, our observations
would start only when the formed features became to be
of this size and the most interesting initial stage of the
condensation process would be hidden. It turns out
anyway that even the last pages of scenario contained
important and unambiguous information. Since hydrogen
is transparent in optical range and absolute difference
between refraction index of solid hydrogen and liquid
helium is not large the method based on the schlieren
photography [7] with the sensitive and high-resolution
CCD camera has been used. The spatial resolution of the
particle registration system was 20–30 �m and depth
resolution was about 3 cm.
While liquid helium was in normal state even at tem-
peratures close to � point the spherical particles with
diameter around 10 �m appeared in a field of view in seve-
ral minutes after the injection termination. The particles
were obviously made of hydrogen; for equimolecular
hyrogen-deuterium mixture in average there were no
definite direction of their motion, whereas for pure deu-
terium whole pattern moved temporarily to the bottom. As
it is seen from Fig. 1 the particles move along slightly
curved trajectories with lateral velocities projections of
few tenths of cm per second. The particles were obviously
entrained by convective flows in liquid helium. Sometimes
they changed sharply the direction of their motion as if
they jumped from one flow to another one. Such a behavior
is the ready solution for the problem of making
quantitative measurements of local flow velocities in
turbulent liquid helium using tracer particles [8]. Indeed
the space resolution of the observation technique and the
size of the fridge windows are close. Thus by focusing the
schlieren system to the cryostat axes and observing simul-
taneously the central area through reciprocally perpen-
dicular pairs of windows one could restore the trajectories
for all particles and such a way obtain the field of flow
velocities in liquid helium.
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation
Fizika Nizkikh Temperatur, 2009, v. 35, No. 3 279
Completely different behavior took place in the case
when the hydrogen injection proceeded into superfluid
helium even if the liquid temperature decreased only a
little below 2.19 K. Almost just after termination of
H2:D2:He mixture injection the very long hairs often being
longer than the window size appeared throughout the su-
perfluid; this was proven by changing of the focusing area
of the observation technique. Such filaments were ob-
served for H2:He mixture as well, though they moved
randomly but predominantly upward to the surface. In the
case of H2:D2 equimolar mixture the motion was pre-
dominately in horizontal direction without any sign of
upflow. The example of the filament is shown in Fig. 2.
Sometimes the filaments were rather short, only few mm
long and practically linear. They had a predominantly ver-
tical position and in the case of H2:He mixture they moved
up with velocity about 0.5 cm/s. The number of hairs
slowly decreased with time and in 20 min they disappeared
from the field of view.
Surprizing and important for applications property of
quantized vortices is their ability of pinning to different
protuberances in apparatus [9]. We used this property for
fixing the formed in superfluid helium filament in a field
of view in order to follow its evolution in time and under
change of conditions. The registration system has been
focused for that purpose to the spot where the low-
temperature optical window’s tube was connected with
the inner wall of a cryostat LHe bath. The example of the
filament «caught» by this way is shown in Fig. 3. This
filament had the length around 3 cm and the diameter,
being the same along whole thread, less than 50 �m. The
temporal behavior of the filament was the same as it has
been theoretically predicted for quantized vortex [9].
Though the filament swung strongly in the flow of the
normal component, its ends were immovable and per-
pendicular to the place of pinning. It was clearly seen that
the filament was levitated in the liquid helium, i.e., it was
consisted of hydrogen-deuterium mixture.
Nevertheless the dilemma still existed, whether the
filaments observed were quantum vortices captured and
kept together separate hydrogen grains as it was con-
sidered recently in Ref. 10, or the quantum vortices
enveloped the fiber-like hydrogen crystals grown inside a
vortex; the enveloping the 16 �m diameter wire by quan-
tized vortex has been considered in Ref. 11. The solution
was simply to heat liquid helium with filaments sus-
pended in it by pulses of pure warm helium gas up to the
temperatures above 2.2 K and to watch what happened
with filaments. The transition to normal state of liquid
helium was easily observed as the start of boiling. It was
stated the hydrogen filaments already grown in superfluid
helium didn’t decay if quantum vortices disappeared, it
allowed to consider them as one-piece fiber-like hyd-
rogen crystals.
280 Fizika Nizkikh Temperatur, 2009, v. 35, No. 3
E.B. Gordon and Y. Okuda
2
1
3
4
5
6
1 cm
Fig. 2. The motion of H2–D2 long filament in superfluid
helium. The time between successive frames is 1 s.
1 cm
1
2
3
4
Fig. 3. The motion in superfluid helium of H2–D2 pinned to
protuberance long filament. The time between successive
frames is 1 s.
1 cm
Fig. 1. The displacement of micron-size H2–D2 particles
drifted with turbulent flows in normal liquid helium, back-
ground is subtracted. The time between successive frames is
0.5 s, the maximal projection of particle velocity to the plane
perpendicular to the observation axis is 0.5 ñm/s.
The aging both in superfluid and in normal states re-
vealed a tendency to filament thickening and lengthening.
However at temperatures higher than T� the ends of fila-
ments were not pinned to some places anymore and they
were moving in a liquid freely. Eventually the fibers spliced
to «rope» up to 150 �m thick and it survives liquid helium
evaporation being seen by unaided eye after that [5].
3. The peculiarities of fiber-like crystal growth
in superfluid helium
According to considerations developed in colloidal
chemistry and valid for every dispersed particles sus-
pended in a liquid the maximal size of separate particles
formed in a liquid is defined by balance between the
coalescence forces in the spot of particles mutual contact
and the fluctuations of liquid action to particles dest-
roying such a contact (see Fig. 4,a). The fluctuations
which values are governed by the ratio of particle’s sur-
face to its volume are responsible for Brownian motion in
liquid. For nonspherical, prolonged particles the limiting
volume of particle should be even less because the sur-
face-to-volume ratio for them is more than for spherical
ones (Fig. 4,b). For this reason even dendrite crystals in
normal liquid have to grow from the end appending
step-by-step the short fragments (Fig. 4,c). In quantum
vortices the prolonged particles are kept directed along
the vortex axes, i.e. coaxial to each other, thus even for
the compounds of isotropic nature the formation of
fiber-like structures from long enough fragments is quite
possible (Fig. 4,d).
As for the condensation of small particles — atoms,
molecules and agglomerates — from liquid helium bulk
on the surface of filaments, there are no specificity of
helium here because the impurity–impurity interaction
ever stronger than impurity–helium interaction. The same
one may say about interaction of two filaments originated
from different vortices, the crossing them is to be fol-
lowed by their reciprocal rotation up to splicing along
their total length because that will gain a lot of energy.
That is the reason for appearance of more thick and more
long (last is due to mismatching the fragments lengths)
fibers.
It is worth to say that filament-like structures (worms)
made of impurities have been already observed in super-
fluid helium [for instance, 12] but nobody connected their
appearance with quantized vortices so far.
4. The promises
One of the declared promises for nanowires and
nanotubes applications is the production of superstrong
ropes from them. The idea is taken from silk and spider’s
web and it is based upon as the practical absence of the
crystal structure faults in nanoobjects as the strong, due to
small radius of curvature, lattice squeezing by surface
tension preventing dislocation exit to a surface, i.e. mi-
crocrack formation. In our experiments such a rope has
been already produced. Though the rope described above
was made of weakly bound hydrogen in the absence of
structural faults it should lift the weight of 50 g and its
length is already sufficiently long both for study and for
applications.
The creation of superstrong ropes is important but far
from being only stimulus for nanowires study. Quantum
wires and quantum dots are attractive objects for basic
science [13]. From the viewpoint of applied science na-
nowires can be used to build the next generation of com-
puting devices. Chemically doped semiconductor nano-
wires of p type and n type have already been created. The
conducting nanowires offer the possibility of connecting
molecular-scale entities in a molecular computer as well
as in flexible flat-screen displays.
The progress in study and application of nanowires is
restrained by their high price, low productivity of manu-
facturing and difficulties of manipulations. A suspended
nanowire used to be produced by chemical etching of a
bigger wire, or bombarding a bigger wire with some
highly energetic particles (atoms or molecules). Another
way to produce a suspended nanowire is to indent the tip
of a scanning tunneling microscope in the surface of a
metal near the melting point, and retract it. Of course,
such a limited production can not be a base for industrial
method.
Nanowire growth in quantized vortices makes it pos-
sible not only to do their production cheaper and more
productive but due to its universality may substantially
expand the variety of these promising objects of nano-
technology. The vortex ability of pinning to any protu-
berance allows growing the wires attached to the tips of
needles intentionally installed in active zone; these need-
les would be served as pincers for manipulation by nano-
wires. Important advantage of given approach is the fea-
sibility to grow a few cm long wires.
As it was already stated the quantized vortices play a
specific role only at first stage of the impurity coalescence
Catalysis of impurities coalescence by quantized vortices in superfluid helium with nanofilaments formation
Fizika Nizkikh Temperatur, 2009, v. 35, No. 3 281
a b
c d
Fig. 4. To the explanation of mechanism of fiber-like crystals
growth.
process. It is profitable at that stage to use small densities
of source material — atoms, molecules and agglomerates
in order to keep the rate of filaments growth inside
quantum vortices much larger than the rate of filament
thickening as at the account of an impurity sedimentation
from the bulk of liquid on their surface as due to entangling
the separate filaments into the rope. In this case up to the
exhaust of initial material the filaments will remain thin.
To realize what method one has to apply for supply the
material for nanowire production into superfluid helium let
estimate with what amounts of matter we should deal. Let
we are going to grow 10 filaments of 3 cm length with
10
3
atoms in a cross-section, that corresponds to diameter
about 10 nm. Thus, we should embed to superfluid helium
about 10
12
atoms; that amount can be ablate from solid
target placed inside of liquid by laser pulse with the energy
around 1 �J. At any case that is no problem to create so
small number of particles.
It is difficult to say something definite about the
crystalline structure of thin filaments formed such a way,
but one could expect the enhanced probability for amor-
phous structure appearance. Both low temperature of coa-
lesced particles and abnormally high removal of coa-
lescence heat by superfluid helium promote stabilization
particles just at the place of primary contact.
The further thickenning of filaments is convenient to
carry out in normal liquid helium to prevent the new
quantized vortices appearance. The particles neccessary
for that could be introduced either by embedding atoms
and molecules from a gas as we did in Ref. 6 or by laser
ablation from target submerged in liquid helium; in the
case of metals the effective method of cathode sputtering
in the spark organized in liquid can be used. It is im-
portant that the material sedimented to filament primarily
grown in a core of quantized vortex could be different
from filament material, and multi-layer filament-like
structure being one-dimensional analog of epitaxial film
may be created. Besides the primary nanofiber could be
built up from volatile material, hydrogen for example, in
order to obtain, after the core evaporation, the nanotube
made of given material.
Impurity particles stabilization in a core of quantized
vortex lengthens the time of their possible contact, that
facilitates low-temperature tunneling chemical reactions
proceeding in case of chemically active species. If the
impurity fragments captured to vortex have enough large
length the time of contact may be indefinitely large. In
principle an aligned polymer may be grown in quantized
vortex such a way.
The experiments on nickel wires growth seems to be of
top-priority. Nanowires made of nickel widely studied
[13]; nickel ferromagnetism allows wire levitation in
liquid helium with using magnetic field: as it follows
from barometric formula at temperature 1.5 K the en-
sembles consisted of less than 10
4
atoms are insensitive to
gravity, whereas bigger agglomerates of nickel display
already ferromagnetism and can be suspended by mag-
netic field. Such experiments are in progress in Cherno-
golovka group. The fact of nickel nanowire formation at
the top of each from four steel needles mounted near the
zone of a spark disrupted from nickel cathode will be
registered by leakage current from the needle.
5. Conclusion
Above suggestions and experimental results confirm
the existence of new phenomenon of catalysis of impu-
rities condensation in superfluid helium by quantized
vortices. That phenomenon results in increasing by many
orders of magnitude the rate of coalescence process and
in formation of filament-like structures having primarily
nanothickness. Since that fact should be valid for any
impurity the phenomenon may be used as a base for the
universal method for nanowires and nanotubes produ-
cing. Due to small matter consumption — 1 cc of the
material is sufficient for the production of nanowires with
total length of 10
7
km — the usage of principally expen-
sive low-temperature technique is competitive with other
methods, especially if one keeps in mind that liquid he-
lium gives itself deep cryogenic purification from any
contamination, usually that is realizes by expensive
high-vacuum chambers and pumps applications.
Apart from the possible applications in industry the
phenomenon under consideration is of significant interest
for basic problems of low temperature physics and che-
mistry. The possibility to rule the loaded by impurities
quantized vortices by using outer fields — magnetic,
gravitational, etc. — seems attractive. The feasibility to
create in quantized vortex at very low temperature the
linear chain of spin-aligned atoms, in particular hydrogen
atoms, makes it possible to elongate the ensemble lifetime
at the account of three-body recombination retardation.
Nowadays there are many speculations on existence at
very low temperature of liquid and even superfluid state
in small hydrogen clusters [14]. The creation of thin but
simultaneously long hydrogen fibers where such a phe-
nomena should take place together with real mass transfer
will give a chance to reveal real fingerprints of super-
fluidity or simply fluidity provided they will take place.
The core of quantized vortices is unique nano-reactor for
low-temperature tunneling chemical reactions.
This work was supported in part by Russian Foundation
for Basic Researches grant #07-03-00393. The authors are
grateful to A.V. Karabulin for technical assistance and to
Profs. I. Silvera (Harvard University), A. Weis (Fribourg
University), and Y. Kagan (Kurchatov Centre) for valuable
discussions.
282 Fizika Nizkikh Temperatur, 2009, v. 35, No. 3
E.B. Gordon and Y. Okuda
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bridge University Press, UK (1991).
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